Subtracting Geometry?
You can use a Boolean modifier.

For example, adding a boolean modifier to a sphere with the operation set to Difference, the parts of the sphere which intersect the object specified in the modifier will be subtracted.



As a bonus, a quick way to select an object for a modifier (or anywhere a similar selection interface is used) is by pressing E while hovering over the object selection drop down and clicking on the desired object in the 3D view.